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 The floating of magnetic material above a superconductor can be explained based on the principle known as Meissner effect.

Temperature below its Critical Temperature( Tc ) a superconductor will not allow any magnetic field to  enter it. This is because microscopic magnetic dipoles are induced in the superconductor which oppose the applied field. This induced field  repels the source of the applied field and  consequently repel the magnet associated with that field.This may cause a magnet  placed on top of the superconductor when the superconductor was above its Critical Temperature, and then it was cooled down to below Tc, the superconductor would then exclude the magnetic field of the magnet. This can be seen clearly as the  magnet itself is repelled, and thus is levitated above the superconductor, if the  force of repulsion must exceed the magnet's weight. This magnetic repulsion phenomena is called the Meissner Effect .